 99278 Simon B.
 A FeynmanKac Formula for Unbounded Semigroups
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Jul 26, 99

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Abstract. We prove a FeynmanKac formula for Schr\"odinger
operators with potentials $V(x)$ that obey (for
all $\varepsilon >0$)
\[
V(x) \geq \varepsilon x^2  C_\varepsilon.
\]
Even though $e^{tH}$ is an unbounded operator, any
$\varphi, \psi \in L^2$ with compact support lie in
$D(e^{tH})$ and $\langle \varphi, e^{tH}\psi\rangle$
is given by a FeynmanKac formula.
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